Gorkss has found himself out of favour at Reading in recent weeks and has not featured for Brian McDermott's men since the Premier League defeat to Arsenal in December.
The 31-year-old is thought to be interested in a move away from Reading in search of regular first-team football.
The news has alerted a number of clubs to Gorkss' possible availability before the close of the transfer window.
Leeds are thought to be in the market for a new defender after seeing Alan Tate return to Swansea following a loan spell at Elland Road.
Leeds boss Neil Warnock is a big fan of Gorkss having worked with him during his time in charge of Queens Park Rangers and he is thought to be considering a move to be reunited with the Latvian stopper.